Though geographically Zenzerspitze belongs to the Carnic Alps Main Ridge it is located on one of the northern side ridges. Actually the Zenzerspitze ridge is the first one counted coming from west and it commands views down into the Lesachtal and Pustertal Valleys that are comparable to those from the westernmost Carnic Alps summit, Helm (Monte Elmo). It is a very popular hiking and ski tour destination, often climbed in conjunction with Hollbrucker Spitze, Hornischegg and Füllhorn to its south-west.
The mountain must have been of strategic importance during World War I, though which importance that might have been, I'm at a loss to explain. Surely enough the location at the junction of two valleys was important but how can you explain the tiny WW I position, which has "windows" just wide enough to put a rifle barrel through? The enemy must have been real close to be killed from there. I assume the position was meant to secure a supply trail to Hochgränten Pass (located to the south between Hollbrucker Spitze and Demut / La Mutta), a heavily fought for passage in the main ridge. There are two trails near the top - the main one cutting through the eastern slope of Zenzerspitze while the eastern one makes for the summit itself. This latter trail is rather overgrown so the best way would be to take the main trail and climb Zenzerspitze from the south across a beautiful grass ridge. Also two ascent routes lead to the summit, both starting at the village of Hollbruck in the Tyrol Gailtal Valley. One takes the northern ridge approach across the Eggwiesen Meadows, the other heading south through Hollbrucker Tal to climb the mountain along its southern ridge. Both approaches can be easily combined with an ascent of Hollbrucker Spitze. A third route starts at Leckfeldalm, which can be reached by car and heads along the main ridge starting at Füllhorn.
"In mathematics you don't understand things. You just get used to them."
--Johann von Neumann